The concept of a line digraph is generalized to that of a directed path graph. The directed path graph Pₖ(D) of a digraph D is obtained by representing the directed paths on k vertices of D by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in D form a directed path on k+1 vertices or form a directed cycle on k vertices in D. In this introductory paper several properties of P₃(D) are studied, in particular with respect to isomorphism and traversability. In our main results, we characterize all digraphs D with P₃(D) ≅ D, we show that P₃(D₁) ≅ P₃(D₂) "almost always" implies D₁ ≅ D₂, and we characterize all digraphs with Eulerian or Hamiltonian P₃-graphs.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1170,
author = {Hajo Broersma and Xueliang Li},
title = {Isomorphisms and traversability of directed path graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {22},
year = {2002},
pages = {215-228},
zbl = {1029.05129},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1170}
}
Hajo Broersma; Xueliang Li. Isomorphisms and traversability of directed path graphs. Discussiones Mathematicae Graph Theory, Tome 22 (2002) pp. 215-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1170/
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